MPHE-026 Solved Assignment July 2025 | ELEMENTS OF REACTOR PHYSICS | IGNOU MSCPH

Q1. Answer the following:

(a)) Calculate the macroscopic scattering cross section for natural uranium. Given ρ = 18.9 g/cm³, percentage weight of 235 U in natural uranium is 0.713; the rest being 238 U. The scattering cross sections for 235 U and 238 U isotopes being 15 b and 13.8 b, respectively. (200 words)
(b)) Distinguish between prompt and delayed neutrons released in fission and discuss their importance. (200 words)
(c)) The average number of neutrons produced per fission is 2.5. What would happen in a second, if every neutron released in fission causes another fission? Assume a generation time of 0.1 second. (200 words)
(d) i)) What is the difference between slowing down density and flux of neutrons? (80 words)
(d) ii)) If the reference neutron energy is 10 MeV, calculate the lethargy at 200 keV, and 0.025 eV? (120 words)
(e)) Discuss the concept of breeding and doubling time and describe how abundant fertile actinides could be converted to excellent fissile actinides. (200 words)

Key Points:

Macroscopic scattering cross section (Σ_s) is the sum of (N_i × σ_s,i) for each isotope in a material.
Prompt neutrons are emitted instantly from fission (~99.3%) and cause rapid criticality if uncontrolled.
Delayed neutrons are emitted by fission product decay (~0.7%) and are essential for reactor control by extending generation time.
Neutron population grows exponentially as N = N₀ × νⁿ, where ν is neutrons per fission and n is generations.

Answer: This response comprehensively addresses key concepts in reactor physics, including the calculation of macroscopic cross sections for natural uranium, distinguishing between prompt and delayed neutrons and their importance in reactor control, analyzing neutron population growth in a hypothetical scenario, defining slowing down density and neutron flux, calculating neutron lethargy, and explaining the principles of breeding and doubling time in nuclear reactors. Each section draws upon fundamental...

Q2. Answer the following:

(a)) Define LAB and CM coordinate frames of reference used to study the kinematics of two- body collision. Obtain an expression of kinetic energy of a neutron after collision in the LAB system. (200 words)
(b)) A 2.6 MeV neutron collides with hydrogen. Calculate the probability that the energy of neutron is within the energy range 0.63 and 0.75 MeV after collision? If a neutron loses 0.75 MeV in LAB system, what is the scattering angle in the CM system? (200 words)
(c)) Derive an expression of average logarithmic energy decrement per collision (ξ). Hence, show that for large mass number, it is independent of energy. Using this formula, plot average logarithmic energy decrement for different nuclides of mass number A. (400 words)
(d)) If a 10 MeV neutron is collided with 238 U nuclide, compare the average energy loss of neuron if they undergo a) inelastic scattering and b) elastic scattering. (200 words)

Key Points:

LAB frame: Target nucleus at rest; CM frame: Center of mass of colliding system at rest, simplifying analysis.
Neutron kinetic energy after elastic collision in LAB: E' = E₀ * (1/2) * [1 + α + (1-α)cosψ], where α = [(A-1)/(A+1)]².
For neutron-hydrogen collision (A=1), α=0; final energy E' is uniformly distributed between 0 and initial energy E₀.
Average logarithmic energy decrement (ξ) quantifies average fractional energy loss per elastic collision: ξ = <ln(E₀/E')>.

Answer: The study of two-body collisions in nuclear physics often employs two primary coordinate frames: the Laboratory (LAB) frame and the Center-of-Mass (CM) frame. These frames offer different perspectives that simplify the analysis of particle interactions. In the LAB frame, the observer is considered stationary, and the target nucleus is initially at rest. This frame directly corresponds to experimental setups and measurements. Conversely, the CM frame is a non-inertial reference system where the ...

Q3. Answer the following:

(a)) Define angular neutron flux and angular current density. The neutron flux at a particular location in a reactor core is 1×1014 neutrons cm-2s-1. What is the average density (inneutrons cm-3) of the thermal neutrons at the same location in the core? (200 words)
(b)) Write the basic assumptions made to derive the transport equation. Hence, derive the Boltzmann transport equation for a multiplying system in terms of neutron flux. (400 words)
(c)) Using spherical harmonics method for a non- multiplying 1-D plane geometry, write the exact infinite coupled equations. Hence for a large non-absorbing system, obtain equations under P₁ approximation. Discuss the limitations of PN approximation. (200 words)
(d)) Discuss the initial, boundary and source conditions. (200 words)

Key Points:

Angular neutron flux: Rate of neutrons crossing unit area per unit solid angle (neutrons cm⁻²s⁻¹sr⁻¹).
Angular current density: Vector flow of neutrons per unit solid angle (Ω * angular flux).
Neutron density (n) = Neutron flux (Φ) / Average speed (v); for thermal neutrons, v ≈ 2.2×10⁵ cm/s.
Boltzmann equation assumptions: Point neutrons, instantaneous interactions, no neutron-neutron interactions, conservation of neutrons.

Answer: This response comprehensively addresses the fundamental concepts of neutron transport theory, including definitions of angular neutron flux and current density, derivation of the Boltzmann transport equation, application of the spherical harmonics method (PN approximation) in 1-D plane geometry, and a discussion of initial, boundary, and source conditions in reactor physics, as per the MPHE-026 course curriculum.

Q4. Answer the following:

(a)) For an arbitrary volume V of material in which one speed neutrons interacts with medium nuclei, if n(r,t) is the neutron density at and at time t, obtain the equation of continuity. Also obtained equation for steady state. (200 words)
(b)) The scattering cross-section of Carbon at 1 eV is 4.8 barn. Estimate the diffusion coefficient of Carbon. Assume that ∑a is almost negligible. (200 words)
(c)) Write two-group criticality condition for a bare homogeneous reactor. Using this equation, show that the six factor criticality condition for two group theory is given by ηf p∈Pf Pt = 1.The symbols have their usual meanings. (400 words)
(d)) Write the Fermi-age critical equation for a bare reactor based on continuous slowing down model. Reduce it to two- group critical equation for large assemblies (for small values of B). (200 words)

Key Points:

Neutron continuity equation: (1/v)∂φ/∂t = D∇²φ - Σaφ + S.
Steady-state continuity: D∇²φ - Σaφ + S = 0 (no time change).
Diffusion coefficient D ≈ 1/(3Σs) when absorption is negligible and scattering is isotropic.
Two-group criticality condition for bare reactor: 1 = (νΣf₁ + (νΣf₂Σs₁₂) / (D₂B² + Σa₂)) / (D₁B² + ΣR₁).

Answer: **(a) Equation of Continuity for Neutrons and Steady State Condition** The neutron continuity equation is a fundamental principle in reactor physics, representing the conservation of neutrons within an arbitrary volume V. It states that the time rate of change of the neutron population within V is equal to the net rate of production minus the net rate of loss (absorption and leakage) of neutrons. Consider an arbitrary volume V in a material where one-speed neutrons interact with medium nuclei....

MPHE-026 Solved Assignment — July 2025

ELEMENTS OF REACTOR PHYSICS | IGNOU Master of Science (Physics) Programme (MSCPH)

MPHE-026—July 2025

ELEMENTS OF REACTOR PHYSICS

Questions & Answers

Download Study Materials

Related Courses

MPHE-026 Assignment Questions — July 2025

Q1. Answer the following:

Q2. Answer the following:

Q3. Answer the following:

Q4. Answer the following:

More MPHE-026 Solved Materials